Airfoil Optimization with Isogeometric Collocation Based on Potential Flow Model

The airfoil optimization design based on numerical calculation of aerodynamic performance can reduce the cost and shorten the design cycle, which has gradually become the mainstream of airfoil design. This paper presents an optimization method for airfoils based on the potential flow model utilizing the isogeometric collocation method. Firstly, the velocity potential of the potential flow model under an ideal incompressible flow is solved by using the isogeometric collocation method. Then, the airfoil’s aerodynamic characteristic index, e.g., lift-to-drag ratio, is calculated based on the Blade Element Theory. Finally, an objective function is formulated to maximize the lift-to-drag ratio and minimize the fitting error. Various optimization methods are then employed to obtain airfoils optimized for both aerodynamic performance and shape smoothness. The NURBS representations of the initial airfoils are acquired by fitting the three types of airfoil data points by the Progressive Iterative Approximation method in the experiment, and the optimization results show that the proposed method not only maintains the airfoil's characteristics and smoothness, but also significantly improves the lift-to-drag ratio.